So I checked with chess.com's engine (I don't keep an engine installed on my desktop anymore) which I don't know the particulars of (is their engine based on open source Stockfish or Komodo which they now own?), but at 34 ply it evaluates -0.66 for black after Rxg1+ Kxg1 Kf7, but interestingly, after the initial rook exchange. it drops the eval to about half a pawn, but it goes steadily up from there each move, so I think maybe it's just a horizon issue.
It's next recommended move for white is b4, and after b4 cxb4 cxb4 it gives black -1.72 at 40 ply, which is even better than the advantage is gives with rooks on the board (-1.25 at 33 ply) in the initial position.
The cool part is, if somebody analyzes this endgame with an engine, they would probably see a -1.25 drop to -0.66 and just stop right there and find a better branch, but the engine figures it out a little down the line 
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Yes , I was Asking for evaluation of 1...Qxc3+ .
Isn't Black crushing White already? ...Qxc3+?? just gives away the Queen after the obvious bxc3 right? I think Black just has to sit tight and convert the position into a win. As @DaddyReza noted, just move the Queen to another square: ...Qa6!? looks bad for White. However, other developing ideas such as ...Nc6 look good for Black too. My evaluation for Qxc3+ is that it is impatient and probably just a blunder (maybe I'm missing something? I don't know).
Here are my thoughts on the position:
Pawn structure - Black is much better. Black has two pawn islands and White has three. Plus, Black's "small island" is a deep pawn only two ranks from promotion (on b3). Compare this to White's pawns sitting far back on their 2nd or 3rd rank with the exception of the doubled h-pawns, but Black's King safely blocks the promotion square, so the advanced pawns are of little danger to Black.
Piece activity - I like Black better here too. White's King is biding its time in the center (somewhat dangerous with Queens on the board, but perhaps okay if an endgame arises soon), but Black's King has an active role of stopping White's h-pawns from advancing/promoting. The open a-file is controlled by Black. True, White may gain control of the c-file, but I think the a-file has more penetration threats. Black can infiltrate on the a-file faster than White can on the c-file. I won't address every piece, but White's are clustered on the bottom right of the board, not doing much, but Black's are more active.
I realize that my assessment is more positional in description, but I think White is already on the verge of being lost if not already; of course, Qxc3+?? just throws away the advantage. Additionally, I noted how White's King isn't ideally placed with Queens on the board. White wants a Queen trade and I'm sure White would ecstatic to get the Queen for only a Rook.
I somehow overlooked that post but whatever I can answer it now ... black's position is worse Than You thought , white's chances on kingside effect Game More Than You thought . For example , black cant play Qa6 Because g6 is hanging ( Qxg6 ) with serious threads . Only move I could play Except Qxc3 was Qe8 , which is very Complex . Qxc3 was A dubious move at most , and A practical play Given OTB situation ( at that time , my opponent only had 5 minutes left on Clock , I had 9 ) ...
I don't think so. Black's attack is still faster and the g6 pawn isn't that important with White's vulnerable King in the center. if ...Qa6 Qxg6!? (which looks strong at a glance, but I don't think there is a quick enough attack White can follow with) then just ...Qa2 to infiltrate and I think Black is quicker. It isn't too difficult to find actually: given that one reasons through the advantages and disadvantages I noted several posts ago.